SA3: Exponents

Exponential growth can be visualized so many different ways. This SA activity will play with the pow function and explore exponents in p5.js.

This activity assumes that the skills from SA2 were introduced (if-else, logical operators, random(), text(), rect(), variables, loop, etc.). Make sure that the pow function is introduced (2^x will not work). This week may be a good time to introduce for loops as well.

Below are a few ideas for projects to explore powers. Learners may come up with their own ideas, or they may want to modify one of the examples below. Save work often and make sure learners know that looping with exponents can freeze up a machine (know keyboard shortcuts).

Diameter Growth

  • Create an animation that draws circles that sequentially double in diameter.
  • Make something random in the code.
  • Print out the diameter.
  • What is the function for this growth?
  • Example Code at p5.js.

See the Pen 2xdiameter by Sophia (@fractalkitty) on CodePen.

Inquiry with a Tree Fractal

  • Use this Example Code and figure out what does what (also in Codepen below).
  • What exponential growth is shown?
  • What happens if you change the values?

See the Pen QuadTree by Sophia (@fractalkitty) on CodePen.

3^x Squares

  • Create code that animates 3^x.
  • Add a text box that gives the quantity.
  • Randomize something in the code.
  • Create a condition to stop the loop.
  • Example Code at p5.js.

See the Pen 3xrect by Sophia (@fractalkitty) on CodePen.

Example Concepts: Exponents, variables, coordinate planes, ordered pairs, conditions, loops, random numbers, functions, etc..

Other tips:

  • Google has a RGB color picker if searched for on Google.
  • Keep it simple – remind learners to start simple and then build on their ideas if they have time.
  • Modifying example code into something new is a great way to get started.
  • Know the keyboard shortcuts to stop the code.

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Week 44: Conics, Orbits, and Projectile Motion

You don’t have to be in high school math to play with conics, orbits, and projectile motion. This week (or month) learners can play with projectile motion, orbits, and conics sections with the activities below:

1.) Slicing cones

  • Learners can mold cones with clay and slice to see the possible shapes. This will give circles, ellipses, parabolas, and hyperbolas.
  • Create a cone sculpture with an intersecting plane using paper, string, pipe cleaners, or other mediums.
  • Try John Sharp’s sliceform template.
  • Check out this Conics Geogebra tool by Irina Boyadzhiev.

2.) Observe parabolas through projectiles

  • Create a straw rocket (don’t aim it at someone) and take slow motion videos of their flight and observe the curve that is created. For a template and activity, go to NASA’s website here. Look at various launch angles and analyze the differences and similarities in curves.
  • Create a water balloon launcher with PVC pipes (or other parent/teacher approved apparatuses). Record their launches and analyze. (Water rockets are also fun.)
  • Play with a garden hose and the curves created by shooting water up into the air.
  • Play with the PhET simulator.
Rocket Launch

3.) Play with ellipses and circles through gravity

  • Use tacks and string to create ellipses (2 tacks) and circles (1 tack or compass). Create an abstract work of art with these tools.
  • Play with this gravity simulator by the NSTMF (really fun!)
  • Universe Sandbox is a program that costs money, but is excellent for playing with orbits and answering a lot of learners’ “what-if’s.” I love, love, love this tool!
  • JPL learning activities are here.
  • Use a large piece of elastic cloth and place weights in it. See if you can create orbits with marbles. We have found that a hula hoop works with swimsuit material. Here is a video as well.
  • Take time to get outside and observe the planets, comets, and astronomy that is with us every day.

There are so many other ways to play with these curves, so experiment, draw/paint, and enjoy.

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Week 43: Circles and Art

Circles are so much fun! This week I encourage learners to get out their compasses or a circle to trace and start making patterns on paper. Patterns with circles can start simple, but can also get really complex. You can combine your compass with a straight edge and get amazing patterns and tiles. Try intersecting circles and then placing your compass at intersections and adding more circles. Shading with markers, ink, or colored pencils can make beautiful stained glass-like mosaics.

Here are some ideas to play with circles and art:

  • The Metropolitan Museum of art has a great activity here to take a look at Islamic art and geometry.
  • Cut out some of your patterns to make a puzzle.
  • Use tissue paper and make a see-through design on wax paper.
  • Go big with string and chalk outside for your designs!
  • Dip the top of a can or cup in paint and use it to create circle patterns on boards or fabric.
  • Try playing with the negative space within the art – see how it changes the tiles and overall appearance.
  • Use a digital drawing or design app and play with color pallets and design.
  • Try adding details and embellish.
  • Play with the Girih app (costs money) from the Apple app store.
  • Play with an app: https://girihdesigner.com/.

I made tiles for my kids to play with and we’ve been having a blast:

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